Skip to main content

Advertisement

Log in

Contour propagation using non-uniform cubic B-splines for lung tumor delineation in 4D-CT

  • Original Article
  • Published:
International Journal of Computer Assisted Radiology and Surgery Aims and scope Submit manuscript

Abstract

Purpose

Accurate target delineation is a critical step in radiotherapy. In this study, a robust contour propagation method is proposed to help physicians delineate lung tumors in four-dimensional computer tomography (4D-CT) images efficiently and accurately.

Methods

The proposed method starts with manually delineated contours on the reference phase. Each contour is fitted by a non-uniform cubic B-spline curve, and its deformation on the target phase is achieved by moving its control vertexes such that the intensity similarity between the two contours is maximized. Since contour is usually the boundary of lesion or tissue which may deform quite differently from the tissues outside the boundary, the proposed method treats each contour as a deformable entity, a non-uniform cubic B-spline curve, and focuses on the registration of contour entity instead of the entire image to avoid the deformation of contour to be smoothed by its surrounding tissues, meanwhile to greatly reduce the time consumption while keeping the accuracy of the contour propagation. Eighteen 4D-CT cases with 444 gross tumor volume (GTV) contours manually delineated slice by slice on the maximal inhale and exhale phases are used to verify the proposed method.

Results

The Jaccard similarity coefficient (JSC) between the propagated GTV and the manually delineated GTV is 0.885 ± 0.026, and the Hausdorff distance (HD) is \(2.93\,\pm \,0.93\) mm. In addition, the time for propagating GTV to all the phases is 3.67 ± 3.41 minutes. The results are better than fast adaptive stochastic gradient descent (FASGD) B-spline method, 3D+t B-spline method and diffeomorphic Demons method.

Conclusions

The proposed method is useful to help physicians delineate target volumes efficiently and accurately.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Min Y, Neylon J, Shah A, Meeks S, Lee P, Kupelian P, Santhanam AP (2014) 4D-CT Lung registration using anatomy-based multi-level multi-resolution optical flow analysis and thin-plate splines. Int J Comput Assist Radiol Surg 9(5):875–889. doi:10.1007/s11548-013-0975-7

    Article  PubMed  Google Scholar 

  2. Wu G, Wang Q, Lian J, Shen D (2013) Estimating the 4D respiratory lung motion by spatiotemporal registration and super-resolution image reconstruction. Med Phys 40(3):031710. doi:10.1118/1.4790689

    Article  PubMed  PubMed Central  Google Scholar 

  3. Docef A, Murphy MJ (2008) Reconstruction of 4D deformed CT for moving anatomy. Int J Comput Assist Radiol Surg 3(6):591–598. doi:10.1007/s11548-008-0266-x

    Article  Google Scholar 

  4. Gaede S, Olsthoorn J, Louie AV, Palma D, Yu E, Yaremko B, Ahmad B, Chen J, Bzdusek K, Rodrigues G (2011) An evaluation of an automated 4D-CT contour propagation tool to define an internal gross tumour volume for lung cancer radiotherapy. Radiother Oncol 101(2):322–328. doi:10.1016/j.radonc.2011.08.036

    Article  PubMed  Google Scholar 

  5. Jang SS, Huh GJ, Park SY, Yang PS, Cho E (2015) Usefulness of target delineation based on the two extreme phases of a four-dimensional computed tomography scan in stereotactic body radiation therapy for lung cancer. Thorac Cancer 6(3):239–246. doi:10.1111/1759-7714.12170

    Article  PubMed  PubMed Central  Google Scholar 

  6. Hutchinson A, Bridge P (2015) 4DCT radiotherapy for NSCLC: a review of planning methods. J Radiother Pract 14(01):70–79. doi:10.1017/S1460396914000041

    Article  Google Scholar 

  7. Pan T, Riegel AC, Ahmad MU, Sun X, Chang JY, Luo D (2013) New weighted maximum-intensity-projection images from cine CT for delineation of the lung tumor plus motion. Med Phys 40:061901. doi:10.1118/1.4803534

    Article  PubMed  Google Scholar 

  8. Park K, Huang L, Gagne H, Papiez L (2009) Do maximum intensity projection images truly capture tumor motion? Int J Radiat Oncol Biol Phys 73(2):618–625. doi:10.1016/j.ijrobp.2008.10.008

    Article  PubMed  Google Scholar 

  9. Cai J, Read PW, Baisden JM, Larner JM, Benedict SH, Sheng K (2007) Estimation of error in maximal intensity projection-based internal target volume of lung tumors: a simulation and comparison study using dynamic magnetic resonance imaging. Int J Radiat Oncol Biol Phys 69(3):895–902. doi:10.1016/j.ijrobp.2007.07.2322

    Article  PubMed  Google Scholar 

  10. Martin S, Brophy M, Palma D, Louie AV, Yu E, Yaremko B, Ahmad B, Barron JL, Beauchemin SS, Rodrigues G (2015) A proposed framework for consensus-based lung tumour volume auto-segmentation in 4D computed tomography imaging. Phys Med Biol 60(4):1497. doi:10.1088/0031-9155/60/4/1497

    Article  PubMed  Google Scholar 

  11. Chebrolu VV, Saenz D, Tewatia D, Sethares WA, Cannon G, Paliwal BR (2014) Rapid automated target segmentation and tracking on 4D data without initial contours. Radiol Res Pract. doi:10.1155/2014/547075

    PubMed  PubMed Central  Google Scholar 

  12. Morcos M, Sultanem K, Bahoric B, Stroian G, Deblois F (2011) Evaluation of deformable contour propagation. Med Phys 38(6):3550. doi:10.1118/1.3612226

    Google Scholar 

  13. van Dam IE, de Koste JRvS, Hanna GG, Muirhead R, Slotman BJ, Senan S (2010) Improving target delineation on 4-dimensional CT scans in stage I NSCLC using a deformable registration tool. Radiother Oncol 96(1):67–72. doi:10.1016/j.radonc.2010.05.003

  14. Vercauteren T, Pennec X, Perchant A, Ayache N (2009) Diffeomorphic demons: efficient non-parametric image registration. NeuroImage 45(1):S61–S72. doi:10.1016/j.neuroimage.2008.10.040

    Article  PubMed  Google Scholar 

  15. Allaire S, Pekar V, Hope A, Breen S, Jaffray D (2008) Automatic contour propagation in head and neck IGRT based on 3D salient interest points. Int J Radiat Oncol Biol Phys 72(1):S87. doi:10.1016/j.ijrobp.2008.06.964

    Article  Google Scholar 

  16. Wrangsjö A, Pettersson J, Knutsson H (2005) Non-rigid registration using morphons. In: Kalviainen H, Parkkinen J, Kaarna A (eds) Image analysis. Springer, Berlin Heidelberg, pp 501–510. doi:10.1007/11499145_51

  17. Hardcastle N, Van Elmpt W, De Ruysscher D, Bzdusek K, Tomé WA (2013) Accuracy of deformable image registration for contour propagation in adaptive lung radiotherapy. Radiat Oncol 8(1):243. doi:10.1186/1748-717X-8-243

    Article  PubMed  PubMed Central  Google Scholar 

  18. Thirion J-P (1995) Fast non-rigid matching of 3D medical images. https://hal.inria.fr/inria-00077268/. Accessed 16 Dec 2015

  19. Xie XH, Ma C, Sun Q, Du RX (2013) An improved demon registration with mutual information for non-rigid medical images. In: Hsieh W-H (ed) Applied mechanics and materials. Trans Tech Publication, Zurich, Switzerland, pp 1622–1626. doi:10.4028/www.scientific.net/AMM.284-287.1622

  20. Peroni M, Spadea MF, Riboldi M, Baroni G, Chen GT, Sharp GC (2009) Validation of an automatic contour propagation method for lung cancer 4D adaptive radiation therapy. In: Proceedings of the 6th IEEE international conference on symposium on biomedical imaging: from nano to micro, Boston, Massachusetts, USA, 2009. IEEE, pp 1071–1074. doi:10.1109/ISBI.2009.5193241

  21. Lee S, Wolberg G, Chwa KY, Shin SY (1996) Image metamorphosis with scattered feature constraints. IEEE Trans Vis Comput Graph 2(4):337–354. doi:10.1109/2945.556502

    Article  Google Scholar 

  22. Kumarasiri A, Siddiqui F, Liu C, Yechieli R, Shah M, Pradhan D, Zhong HL, Chetty IJ, Kim J (2014) Deformable image registration based automatic CT-to-CT contour propagation for head and neck adaptive radiotherapy in the routine clinical setting. Med Phys 41(12):121712. doi:10.1118/1.4901409

    Article  PubMed  Google Scholar 

  23. Qiao Y, Lew B, Lelieveldt B, Staring M (2015) Fast automatic step size estimation for gradient descent optimization of image registration. IEEE Trans Med Imaging. doi:10.1109/TMI.2015.2476354

    PubMed  Google Scholar 

  24. Xiong G, Chen C, Chen J, Xie Y, Xing L (2012) Tracking the motion trajectories of junction structures in 4D CT images of the lung. Phys Med Biol 57(15):4905. doi:10.1088/0031-9155/57/15/4905

    Article  PubMed  Google Scholar 

  25. Metz C, Klein S, Schaap M, van Walsum T, Niessen WJ (2011) Nonrigid registration of dynamic medical imaging data using nD+ t B-splines and a groupwise optimization approach. Med Image Anal 15(2):238–249. doi:10.1016/j.media.2010.10.003

    Article  CAS  PubMed  Google Scholar 

  26. Castillo R, Castillo E, Guerra R, Johnson VE, McPhail T, Garg AK, Guerrero T (2009) A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Phys Med Biol 54(7):1849. doi:10.1088/0031-9155/54/7/001

    Article  PubMed  Google Scholar 

  27. Vandemeulebroucke J, Rit S, Kybic J, Clarysse P, Sarrut D (2011) Spatiotemporal motion estimation for respiratory-correlated imaging of the lungs. Med Phys 38(1):166–178. doi:10.1118/1.3523619

    Article  PubMed  Google Scholar 

  28. Liu DC, Nocedal J (1989) On the limited memory BFGS method for large scale optimization. Math Program 45:503–528. doi:10.1007/bf01589116

    Article  Google Scholar 

  29. Schmidt M (2015) L-BFGS for Matlab. http://www.cs.ubc.ca/~schmidtm/Software/minFunc.html. Accessed 16 Dec 2015

  30. Jaccard P (1908) Nouvelles recherches sur la distribution florale. Bull Soc Vaud Sci Nat 44(163):223–270

    Google Scholar 

  31. Huttenlocher DP, Klanderman G, Rucklidge WJ (1993) Comparing images using the Hausdorff distance. IEEE Trans Pattern Anal Mach Intell 15(9):850–863. doi:10.1109/34.232073

  32. Vercauteren T, Pennec X, Perchant A, Ayache N (2007) Non-parametric diffeomorphic image registration with the demons algorithm. In: Medical image computing and computer-assisted intervention-MICCAI 2007. doi:10.1007/978-3-540-75759-7_39

  33. Shamonin D, Bron E, Lelieveldt B, Smits M, Klein S, Staring M (2013) Fast parallel image registration on CPU and GPU for diagnostic classification of Alzheimer’s disease. Front Neuroinform 7:50. doi:10.3389/fninf.2013.00050

    Article  PubMed  Google Scholar 

  34. Klein S, Staring M, Murphy K, Viergever M, Pluim JP (2010) Elastix: a toolbox for intensity-based medical image registration. IEEE Trans Med Imaging 29(1):196–205. doi:10.1109/TMI.2009.2035616

    Article  PubMed  Google Scholar 

  35. Piegl L, Tiller W (1997) The NURBS book, 2nd edn. Springer, Berlin, Heidelberg, New York

    Book  Google Scholar 

  36. De Boor C (1972) On calculating with B-splines. J Approx Theory 6(1):50–62. doi:10.1016/0021-9045(72)90080-9

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank Min Chen, Professor of School of Computer Science and Technology at Huazhong University of Science and Technology, for his helpful opinions and suggestions. We acknowledge the editors and reviewers for their hard work and constructive comments. This research was partially supported by the National Science Foundation of China (61370179), the National Science and Technology Support Project Funds of China (2011BAI12B05), the Fundamental Research Funds for the Central Universities of China, HUST: 2016YXMS086 and CXY12Q030.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renchao Jin.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Ethical standard

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki Declaration and its later amendments or comparable ethical standards.

Informed consent

Informed consent is not needed. Eighteen cases of four-dimensional computer tomography images are used in our study, seven of them are publically available, the informed consent is not needed for them. And the remaining cases are well de-identified so that it is impossible to link the records to the particular individuals. In addition, the patients involved in the remaining cases have deceased, and our study is a retrospective one, so the informed consent is also not needed for them.

Appendices

Appendix 1: Determination of knot vector

Let \({{\varvec{U}}}=\{u_i , i=0,1,\ldots ,n+6\}\) denote the knot vector, where \(u_3 ,u_4 ,\ldots u_{n+3} \) are internal knots since they are inside the domain of definition, and \(u_0 ,u_1 ,u_2 ,u_{n+4} ,u_{n+5} ,u_{n+6} \) are external knots since they are outside the domain of definition. As shown in Eq.  1, \({{\varvec{q}}}^{(0)}=\{{{\varvec{q}}}_i^{(0)} ,i=0,1,\ldots ,n\}\) is fitted by \({{\varvec{p}}}^{(0)}\), such that \({{\varvec{q}}}_i^{(0)} ={{\varvec{p}}}^{(0)}(u_{i+3})\), where \({{\varvec{q}}}_0^{(0)} \) and \({{\varvec{q}}}_n^{(0)}\) are the first and last endpoints, respectively. In order to make \({{\varvec{p}}}^{(0)}\) a closed curve and \(C^{2}\)continuous, the following conditions are satisfied:

$$\begin{aligned} \left\{ {\begin{array}{l} {{\varvec{q}}}_0^{(0)} ={{\varvec{q}}}_n^{(0)} \\ {{\varvec{d}}}_n^{(0)} ={{\varvec{d}}}_0^{(0)} \\ {{\varvec{d}}}_{n+1}^{(0)} ={{\varvec{d}}}_1^{(0)} \\ {{\varvec{d}}}_{n+2}^{(0)} ={{\varvec{d}}}_2^{(0)} \\ \end{array}} \right. . \end{aligned}$$

As shown in Eq. 5, the \(n+1\) internal knots \(u_3 ,u_4 ,\ldots u_{n+3} \) are defined by the chord length method [35], which is widely used and usually performs well.

$$\begin{aligned} \left\{ {\begin{array}{l} u_3 =0 \\ u_b =u_{b-1} +{\left| {{{\varvec{q}}}_{b-3}^{(0)} -{{\varvec{q}}}_{b-4}^{(0)} } \right| }/L,\quad b=4,5,\ldots ,n+3 \\ \\ L =\sum _{i=1}^n {\left| {{{\varvec{q}}}_i^{(0)} -{{\varvec{q}}}_{i-1}^{(0)} } \right| } \\ \end{array}} \right. \end{aligned}$$
(5)

And the six outside knots are

$$\begin{aligned} \left\{ {\begin{array}{l} u_0 =u_n -1 \\ u_1 =u_{n+1} -1 \\ u_2 =u_{n+2} -1 \\ u_{n+4} =u_4 +1 \\ u_{n+5} =u_5 +1 \\ u_{n+6} =u_6 +1 \\ \end{array}} \right. . \end{aligned}$$

When the knot vector \({{\varvec{U}}}\) is defined, \(N_{k,3} (u),k=0,1,\ldots ,n+2\) can be defined by the de Boor–Cox recursion formula [36], namely,

$$\begin{aligned} \left\{ {\begin{array}{l} N_{k,0} (u)=\left\{ {\begin{array}{l} 1\quad \mathrm{if} u\in [u_k ,u_{k+1} ), \\ 0\quad \mathrm{otherwise}. \\ \end{array}} \right. \\ N_{k,h} (u)=\frac{u-u_k }{u_{k+h} -u_k }N_{k,h-1} (u)+\frac{u_{k+h+1} -u}{u_{k+h+1} -u_{k+1} }N_{k+1,h-1} (u)\quad \mathrm{if}h\ge 1 \\ \frac{0}{0}=0 \\ \end{array}} \right. . \end{aligned}$$
Fig. 11
figure 11

Schematic diagram of how to derive the propagated contour on the z-th slice, where u = 0.3, \(\varepsilon \) = 0.25, K = 4

Appendix 2: Slice contours derived from a set of propagated contours

Assume \({{\varvec{p}}}_s^{(0)} \) and \({{\varvec{p}}}_{s+1}^{(0)} \) are the contours on the s-th and (s+1)-th slice of the reference phase, respectively, and their propagated contours are \({{\varvec{p}}}_s \) and \({{\varvec{p}}}_{s+1} \), respectively. Search a point \({{\varvec{p}}}_{s+1} (u)\) on the contour \({{\varvec{p}}}_{s+1} \) such that it is the closest point to \({{\varvec{p}}}_s (0)\). Let K be a sufficiently large positive integer, \(\varepsilon =1/K,k=0,1,2,\ldots K-1\), then K line segments between the points \({{\varvec{p}}}_s (\varepsilon k)\) and points \({{\varvec{p}}}_{s+1} (u+\varepsilon k\hbox { }\bmod \hbox { }1)\) are generated, where mod is the modulo operator. Assume that the target tumor is composed of M contours. Then for every two adjacent contours, K line segments are generated in accordance with the above method, and \(K(M-1)\) line segments are generated in total. The \(K(M-1)\) line segments intersect the z-th slice plane at a series of intersections which are taken as the sampling points, and the contour on the z-th slice is obtained by fitting a non-uniform cubic B-spline curve to these sampling points. The schematic diagram of how to derive the propagated contour on the z-th slice is shown in Fig. 11.

Fig. 12
figure 12

An example of keeping the derived contour closed. a The derived contour is unclosed, and b the closed contour is obtained by replacing line segments with rays. The green curves are manually delineated contours, and the red curves are delineated by the proposed method

Near the top or bottom of the tumor, sometimes the derived contours are unclosed, as shown in Fig. 12a. This can be explained in Fig. 11: if \({{\varvec{p}}}_s \) did not exist, i.e., \({{\varvec{p}}}_{s+1} \) is the highest contour of the tumor, then some line segments between the points \({{\varvec{p}}}_s (\varepsilon k)\) and points \({{\varvec{p}}}_{s+1} (u+\varepsilon k\hbox { }\bmod \hbox { }1)\) would not exist, which would lead to a unclosed contour on the z-th slice. The solution is to replace the line segments between \({{\varvec{p}}}_{s\hbox {+}2} (u+\varepsilon k\hbox { }\bmod \hbox { }1)\) and \({{\varvec{p}}}_{s\hbox {+}1} (\varepsilon k)\) with rays whenever \({{\varvec{p}}}_{s+1} \) is the highest contour. Then the closed contour is obtained as shown in Fig. 12b. A similar strategy is also applied to the lowest contour.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Y., Jin, R., Chen, M. et al. Contour propagation using non-uniform cubic B-splines for lung tumor delineation in 4D-CT. Int J CARS 11, 2139–2151 (2016). https://doi.org/10.1007/s11548-016-1457-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11548-016-1457-5

Keywords

Navigation